The matching problem between functional shapes via a $BV$ penalty term: A $Gamma$-convergence result
The matching problem between functional shapes via a $BV$ penalty term: A $Gamma$-convergence result
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通过 $BV$ 惩罚项的函数形状之间的匹配问题：$Gamma$ 收敛结果
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
A. Trouvé
中科院分区：
文献类型：
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作者：
Giacomo Nardi;Benjamin Charlier;A. Trouvé
本文研究了CITE{ABN}中介绍的函数形状之间匹配模型的一种变体。这样的模型允许比较配备有信号的表面，匹配的能量由表面上信号的$L^2$-范数和一个不同类型的附着项定义。
在这项工作中，我们研究固定几何的问题，这意味着我们优化初始信号(支撑在初始表面上)相对于支撑在不同表面上的目标信号。特别地，我们考虑信号的$BV$或$H^1-罚，而不是它的$L^2$-范数。文中给出了几个数值例子，以证明$BV$-罚金提高了匹配的质量。此外，我们还证明了离散匹配能量向连续匹配能量的$Gamma-收敛结果。
In this paper we study a variant of the matching model between functional shapes introduced in cite{ABN}. Such a model allows to compare surfaces equipped with a signal and the matching energy is defined by the $L^2$-norm of the signal on the surface and a varifold-type attachment term.
In this work we study the problem with fixed geometry which means that we optimize the initial signal (supported on the initial surface) with respect to a target signal supported on a different surface. In particular, we consider a $BV$ or $H^1$-penalty for the signal instead of its $L^2$-norm. Several numerical examples are shown in order to prove that the $BV$-penalty improves the quality of the matching. Moreover, we prove a $Gamma$-convergence result for the discrete matching energy towards the continuous-one.
影响因子：
19.5
作者：
Bauer, Martin;Charon, Nicolas;Hsieh, Hsi-Wei
通讯作者：
Hsieh, Hsi-Wei